Apparatus for sensing liquid flow and pressure in a conduit or open channel and associated

ABSTRACT

An apparatus includes a conduit having a generally circular cross-section, and a liquid flow sensor extending into the conduit so that a liquid contacting portion extends generally parallel to an axis of the conduit and is positioned to extend into an interior of the conduit a first distance. An electromagnetic coil is positioned in the housing for generating a magnetic field within the liquid flow. In addition, the sensor includes a pair of spaced apart electrodes defining a second distance therebetween and being exposed on the liquid contacting portion for generating a signal related to the liquid flow rate. Moreover, the second distance is preferably greater than or equal to about two times the first distance and is greater than or equal to about one-tenth a diameter of the conduit. An open channel embodiment of the invention has a cross-section of a predetermined width and an opening in a bottom wall thereof. A liquid flow sensor is positioned in the opening in the open channel. The liquid flow sensor is as described above. In this embodiment, however, the pair of spaced apart electrodes preferably define a distance therebetween being in a range of about 0.10 to 0.95 times the predetermined width of the open channel. This relationship ensures acceptable accuracy using a relatively compact, lightweight and relatively inexpensive sensor. Method aspects of the invention are also disclosed.

This application is a divisional of Ser. No. 08/641,615 filed on May 1,1996; now U.S. Pat. No. 5,693,892.

FIELD OF THE INVENTION

The present invention relates to the field of sensors, and, moreparticularly, to a sensing apparatus for liquid flow.

BACKGROUND OF THE INVENTION

A magnetic or electromagnetic liquid flow sensor is commonly used fordetermining the flow rate or volumetric flow of a conductive liquid ormedia, such as fresh water or waste water, for example, flowing within aconduit. A magnetic flow sensor operates in accordance with Faraday'sLaw which provides that a moving conductor in a magnetic field generatesa voltage, the amplitude of which is proportional to the velocity of theconductor. For a magnetic flowmeter, the moving conductor is the liquidor media flowing adjacent the flowmeter.

There are two general types of conventional magnetic flow sensors orflowmeters each with its own shortcomings. A first type of magneticflowmeter includes two opposing electromagnetic coils positioned outsideand immediately adjacent a non-ferrous conduit or spool piece. Themagnets generate a magnetic field through the media passing through thenon-ferrous spool piece, while the moving media generates a smallelectrical voltage between a pair of spaced apart electrodes extendinginto the spool piece and contacting the media. The electromagnets aretypically energized with a bipolar waveform of relatively low frequency,and the output voltage of the electrodes is converted by an electricalcircuit into a desired analog or digital signal representing the flowrate. The energizing of coils and processing of the voltage signal istypically performed in a remote or integrally mounted converter.

Conventional magnetic flow meters normally operate with a magnetizingcurrent of typically 100-200 milliamps peak-to-peak, at a frequency oftypically about 5 Hz and at typical bipolar voltage of 20-30 Volts. Thisnormally provides a magnetic field strength which allows the velocitymeasured at the electrodes to be sufficiently weighted to representvolumetric flow with acceptable accuracy. However, the coils must be ofsubstantial size such that the magnetic field covers the complete orsubstantial area of the cross-section of the conduit or spool piece. Inmany cases two relatively heavy coils are required to wrap substantiallyaround the external circumference of the spool piece to provide asuitable magnetic field.

The spool piece of a conventional sensor is typically manufactured fromnon-magnetic material, which is normally a non-magnetic stainless steelfor strength and so that the distribution of the magnetic field is notdisturbed. The complete internal diameter of the spool piece iselectrically insulated with rubber, PTFE or a similar insulatingmaterial, with the electrodes virtually flush with the circular spoolpiece internal diameter. The need for an electrically insulating linerincreases the expense of the flowmeter and, more importantly, should themedia penetrate the liner, electrical noise may overwhelm the relativelysmall output signal of the sensor.

The weight of the electromagnetic coils and the power consumption oftypically greater than 10 VA has other major disadvantages. Namely thecoils cannot be typically encapsulated in solid setting insulationmaterial, since the temperature rise would be too excessive.Accordingly, shock or vibration applied to the sensor may result insignificant movement of the coils relative to the conduit, resulting inchange of calibration and/or inducing vibration errors.

Conventional sensors of the type having the coils on the outside of anon-magnetic spool piece of circular cross-section typically have noform of simple liquid velocity profile conditioning. Errors due tounconditioned irregular velocity profiles within the conduit areinherent in the flow sensing, unless a relatively expensive nozzle orventuri restriction is incorporated in the conduit.

A number of patent references disclose such conventional magneticflowmeters or sensors with coils positioned external to the pipe throughwhich the measured media is flowing. For example, U.S. Pat. No.5,125,276 to Wada discloses a magnetic flowmeter including a pluralityof coils surrounding a measuring pipe which, in turn, may be conductingand further include an electrically insulating lining. A magnetic casingsurrounds the overall assembly. Along these lines, U.S. Pat. No.4,920,795 to Codazzi et al. discloses a non-intrusive magnetic flowmetersensor adjacent an insulated non-magnetic pipe through which a highpressure liquid flows. U.S. Pat. No. 4,409,846 to Ueno discloses amagnetic flowmeter including a non-conductive and non-magnetic pipethrough which the liquid passes.

U.S. Pat. No. 4,290,312 to Kobayashi discloses a magnetic flowmeter alsowith an external coil. The flowmeter includes auxiliary electrodesmounted on the inner wall of the flow tube that are interconnected sothat when the fluid ceases to be symmetrical, a potential difference isdeveloped between the points which are short-circuited to cause thepotential distribution in the tube to assume a distribution close tothat encountered with a flow that is symmetrical thereby alleviating theerror from the non-symmetrical fluid flow.

U.S. Pat. No. 3,620,079 Nosley discloses an embodiment of a flowmeterincluding a housing, a coil positioned within the housing, and a seriesof electrodes on the face of the housing. The electrodes are positionedwithin an imaginary cylinder defined by the interior of the coil. Inother words, the electrodes are spaced relatively close and provide arelatively weak output signal that is susceptible to electrical noise.Similarly, published Japanese patent application no. 55-55475 to Wadadiscloses a flowmeter positioned in the opening of the wall of a pipeformed of magnetic material. The depth of extension of the flat outerface of the sensor into the pipe is relatively small given therelatively large diameter of the pipe. In other words, the spacing ofthe electrodes relating to the overall pipe diameter is also relativelysmall. Accordingly, the sensor may also be subject to electrical noise.

U.S. Pat. No. 4,181,018 to Schmoock discloses a flowmeter including aferromagnetic ring within which a pair of electromagnets are supported.An annular pressure vessel is molded within the ring and encapsulatesthe coils, as well as a pair of opposing electrodes. U.S. Pat. No.4,261,210 to Gardner discloses a flowmeter including an electromagnetformed of a plurality of stacked helically coiled conductive windingsand wherein the electrodes are positioned on the face of the windings.Of further interest, U.S. Pat. No. 3,094,000 to Kass discloses aflowmeter including coils positioned external to the media carrying tubewhich, in turn, is lined with an insulating material. U.S. Pat. No.3,881,350 to Nosley discloses a flowmeter for high pressure fluids,wherein a high pressure fluid is retained within an internal cavity tobalance the high external pressure.

It may also be desirable to obtain a liquid flow rate measurement froman open channel conduit, that is, a conduit having sidewalls and abottom, but which is open along the top. Relating to a flowmeter foropen channel flow measurement, U.S. Pat. No. 3,929,016 to Takeuchi etal. discloses a tubular flowmeter mounted on a dam gate. U.S. Pat. No.4,122,714 to Kobayashi et al. discloses a flowmeter for an open channelincluding a tube of insulation material positioned in the channel withits longitudinal axis normal to the direction of flow. German Pat. No.2,814,853 patent discloses flowmeter for an open channel including threeelectromagnets positioned around the open channel. Unfortunately,conventional sensors for an open channel may be inaccurate, especiallywhere flow rates and liquid levels vary substantially.

A second type of flowmeter is an insertion magnetic flow sensor whichincludes a pair of electrodes and one or more coils in a singleassembly. The sensor assembly is inserted through a media carryingconduit or tube which may be magnetic or non-magnetic. A representativeinsertion type sensor is manufactured by Turbo Instruments Inc. ofOrinda Calif. under the designation MIS 2, for example. See also U.S.Pat. No. 4,459,858 to Marsh which also discloses an insertion typeflowmeter.

Since both a small coil and a small relative distance between electrodescontribute to a low output signal strength confirmed by Faraday's Law,there is a resultant relatively low signal-to-noise ratio. Accordingly,an insertion sensor may be limited to use with relatively clean media ofhigh conductivity and at relatively high velocities. Such a sensor isnot typically sufficiently accurate and/or reliable to measure raw orfiltered sewage or river water, whose high fat content or algae-typecoatings of the electrodes reduces the effective electrical conductivityof the media.

A further disadvantage of the relatively small diameter conventionalinsertion sensors is their correspondingly low magnetic field strength.For this reason a conventional insertion flowmeter is normally insertedsubstantially into the liquid carrying conduit, typically with itselectrodes situated at one-eighth of the pipe internal diameter tomeasure a realistic mean velocity to infer volumetric flow.Unfortunately, low velocities in large pipelines, pipe wall roughness,and unfavorable piping geometry may cause velocity profileirregularities. Then the ratio of the measured velocity at one eighth ofthe internal pipe diameter to the actual mean velocity representing truevolumetric flow can cause unacceptable error. In addition, the necessarysubstantial insertion into the conduit causes sufficient disturbance ofthe flow media to further limit accuracy and repeatability. Theinsertion also limits the media or liquid to that having a relativelylow viscosity and having no sizeable solids or wrap around streamers.

An insertion magnetic sensor for an open channel or non-full pipe flowmeasurement may be used with a level transducer. Unfortunately, such aconfiguration may also be inaccurate because of the relatively smalldistance between the electrodes compared to the size of the open channelor non-full pipe. The relatively low magnetic field strength and thefrequency of energizing current often leads to an unacceptably lowsignal-to-noise ratio. Furthermore, the small size of a conventionalinsertion sensor does not typically allow accurate level sensing at thelocation of the electrodes, and thus requires more complex level sensingremote from the flow sensor.

Unfortunately, both types of conventional flowmeters or sensors operateat relatively low magnetizing currents and relatively low frequencies.In addition, noise is relatively high compared to the small signalvoltages produced at the electrodes. Noise may be caused, for example,by coating of the electrodes or changes in the conductivity of themedia, particularly where wastewater flow is being sensed. Anomalies ofthe velocity profile within the media carrying tube may also reduce theaccuracy for conventional sensors.

SUMMARY OF THE INVENTION

In view of the foregoing background, it is therefore an object of thepresent invention to provide an apparatus and related method foraccurately sensing a liquid flow rate.

It is another object of the present invention to provide an apparatusand related method for sensing a liquid flow rate even with irregularvelocity flow profiles and with varying flow rates.

It is still another object of the present invention to provide anapparatus for sensing liquid flow rate that is readily manufactured andinstalled.

These and other objects, features and advantages of the presentinvention are provided by a first embodiment of the apparatus comprisinga conduit having a generally circular cross-section, and a liquid flowsensor extending into the conduit so that a liquid contacting portionextends generally parallel to an axis of the conduit and is positionedto extend into an interior of the conduit a first distance. Anelectromagnetic coil is positioned in the housing for generating amagnetic field within the liquid flow. In addition, the sensor includesa pair of spaced apart electrodes defining a second distancetherebetween and being exposed on the liquid contacting portion forgenerating a signal related to the liquid flow rate. Moreover, thesecond distance or electrode spacing is preferably greater than or equalto about two times the first distance and is greater than or equal toabout one-tenth a diameter of the conduit. The second distance orspacing between electrodes is also preferably greater than or equal toabout one-tenth of the conduit diameter.

The pair of electrodes are preferably positioned adjacent respectiveopposite edges of the liquid contacting portion of the housing. The pairof electrodes are also preferably positioned to be substantially flushwith an imaginary cylindrical surface defined by an interior of theconduit. Accordingly, a relatively wide spacing of the electrodes isachieved thereby permitting a larger coil and providing enhancedaccuracy and a higher signal-to-noise ratio.

The liquid contacting portion of the housing also preferably comprises agenerally planar central portion and a downwardly sloping annularportion surrounding the central portion. The electrodes preferablyextend outwardly from adjacent portions of the sloping annular portion.Moreover, the outermost portions of the electrodes are preferablysubstantially flush with an imaginary plane defined by the centralportion. These relationships provide effective placement of theelectrodes and position the housing with a desired amount of penetrationinto the interior of the conduit.

The conduit preferably comprises a magnetically permeable material, suchas carbon steel, so that the electromagnetic coil cooperates with themagnetically permeable material to generate the magnetic field in theliquid flow. The liquid flow sensor also preferably further comprisesflux path means for defining a magnetic flux path from the coil andthrough adjacent portions of the conduit. The flux path means may beprovided by a magnetically permeable core positioned within an annularelectromagnetic coil.

Another aspect of the invention relates to excitation of the coil. Inparticular, excitation means may be provided for powering theelectromagnetic coil with a waveform having a peak-to-peak current ofgreater than about 0.7 amps. The excitation means also preferably powersthe coil with power in a range of about 1 to 6 volt amps. Because arelatively strong magnetic field can be created by the sensor excited atthe frequency range and power range described, potting means may beprovided for securing or encapsulating the electromagnetic coil withinthe housing. Accordingly, the sensor may be made more resistant tomechanical shock and vibration.

The apparatus also preferably includes a processor connected to theelectrodes for sensing a signal to determine a flow rate of the liquid.The processor, in turn, preferably comprises output means for generatinga flow rate output based upon a linear logarithmic relationship betweenoutput per unit volume flow versus flow rate.

A grounding electrode may be carried by the housing for contacting theliquid flow. For example, the central portion of the liquid contactingportion may be electrically conductive to provide the groundingelectrode. In addition, the liquid flow sensor preferably furthercomprises liquid velocity profile conditioning means for inducingturbulence in the liquid flow adjacent the electrodes to thereby enhanceaccuracy.

The apparatus may include a liner within the conduit for certainembodiments. The sensor may also be used without a liner, or withoutconcern for whether the liner has been damaged or otherwise admits anyliquid to portions of the conduit. Alternate embodiments of theinvention may include two or more such liquid flow sensors positioned toextend into an interior of the conduit.

Another variation or embodiment of the apparatus comprises an openchannel for carrying a liquid flow. The open channel has a cross-sectionof a predetermined width and an opening in a bottom wall thereof. Theopen channel may have a generally rectangular transverse cross-section.A liquid flow sensor is positioned in the opening in the open channel.The open channel preferably comprises a magnetically permeable materialand the liquid flow sensor is preferably as described above. In thisembodiment, however, the pair of spaced apart electrodes preferablydefine a distance therebetween being in a range of about 0.10 to 0.95times the predetermined width of the open channel. This relationshipensures acceptable accuracy using a relatively compact, lightweight andrelatively inexpensive sensor.

A method aspect of the present invention is for sensing a liquid flowrate and includes the steps of: providing a conduit for carrying aliquid flow, the conduit having a generally circular cross-section andan opening in a sidewall portion; and positioning a liquid flow sensorin the opening in the conduit so that a liquid contacting portionextends generally parallel to an axis of the conduit and extends into aninterior of the conduit a first distance. The liquid flow sensorpreferably further comprises an electromagnetic coil for generating amagnetic field within the liquid flow and a pair of spaced apartelectrodes defining a second distance therebetween and being exposed onthe liquid contacting portion for generating a signal related to theliquid flow rate. In addition, the step of positioning the liquid flowsensor preferably comprises positioning same so that the second distanceor electrode spacing is greater than or equal to about two times thefirst distance and is greater than or equal to about one-tenth adiameter of the conduit.

Another method aspect of the present invention is also for sensing aliquid flow rate and comprises the steps of: providing an open channelfor carrying a flow of liquid to be measured, the open channel having across-section of a predetermined width and an opening in a bottom wallthereof; and positioning a liquid flow sensor in the opening in the openchannel so that a liquid contacting portion extends generally parallelto an axis of the open channel and extends into an interior of the openchannel. The liquid flow sensor further preferably comprises anelectromagnetic coil for generating a magnetic field within the liquidflow, and a pair of spaced apart electrodes being exposed on the liquidcontacting portion for generating a signal related to the liquid flowrate. Moreover, the electrodes preferably define a distance therebetweenbeing in a range of about 0.10 to 0.95 times the predetermined width ofthe open channel.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of the apparatus in accordance with theinvention.

FIG. 2 is an enlarged cross-sectional view taken along lines 2--2 ofFIG. 1.

FIG. 3 is an enlarged cross-section view of a portion of the apparatusas shown in FIG. 2 rotated ninety degrees clockwise.

FIG. 4 is an enlarged cross-sectional view of an embodiment of theliquid flow sensor of the present invention.

FIG. 5 is a schematic block diagram of a coil excitation circuitaccording to the invention.

FIG. 6 is a series of plots of various current and voltage waveformsproduced by the coil excitation circuit of FIG. 5.

FIG. 7 is a cross-sectional view of another embodiment of a liquid flowsensor of the present invention.

FIG. 8 is a top plan view of the sensor embodiment shown in FIG. 7.

FIG. 9 is a longitudinal cross-sectional cross-section view of theapparatus installed in fluid communication with adjacent conduitsections and illustrating the velocity profile conditioning of theinvention.

FIG. 10 is an end view into the apparatus as shown in FIG. 9.

FIG. 11 is a schematic cross-sectional view of the apparatus of thepresent invention implemented in an open channel.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will now be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown. This invention may, however, be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein. Rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout, and prime and double primenotation are used to indicate similar elements in alternativeembodiments.

Referring to FIGS. 1-6, the sensing apparatus 20 according to thepresent invention is first described. The illustrated apparatus 20includes a pair of opposing flow sensors 21, while for otherapplications a single sensor or multiple sensors may be used as would bereadily understood by those skilled in the art. The sensors 21 may beinstalled in existing pipework, either directly or incorporating aconventional saddle of carbon steel, or which may be retro-fitted intoan existing venturi differential pressure flowmeter to replace theventuri with improved flow rangeability and repeatability. For example,four sensors may be installed in a conduit.

The apparatus 20 includes a pair of flanged standpipes 22 connected tothe media carrying tube or conduit 25. A pair of end flanges 27 areconnected to the opposing longitudinal ends of the conduit 25. The endflanges 27 may be deleted in certain embodiment so that the conduit 25ends are suitable for on-site mounting adapters, as would be readilyunderstood by those skilled in the art. The conduit 25, standpipes 22and end flanges 27 may preferably comprise a magnetically permeablematerial, such as carbon steel or other ferrous metals. Such materialsare relatively strong and low cost compared to materials such asstainless steel, for example.

An electrical junction box 26 facilitates connections of the coils 32 ofthe flow sensors 21 to be connected in series and their electrodes 35 tobe connected in parallel to improve the accuracy of liquid flowmeasurement, particularly for non-uniform velocity profiles within theconduit 25 as will be described in greater detail below. The coils 32and electrodes 35 are connected to the schematically illustratedprocessor 30 and coil excitation means or circuit 39, the operation ofwhich is also described in greater detail below.

The flow sensor 21 includes a housing 34 having a liquid contactingportion 37 and an electromagnetic coil 32 positioned within the housing.The housing 34, in turn, is positioned within the standpipe 22 so thatthe coil 32 produces relatively high magnetic fields, illustrated by thedotted field lines 29, in cooperation with the magnetically permeableconduit 25 and a central soft iron core 40 positioned within the coil32. For example, the magnetic field of a large portion of the areaadjacent the electrodes 35 and extending into the conduit 25 ispreferably greater than about 10 milligauss. The relatively highstrength magnetic field is projected into the flow of liquid and issubsequently attracted and bent towards the carbon steel sidewall of theconduit 25. The shape of the magnetic field represented by field lines29 is desirably such that the media velocity sensed at the electrodes 35represents the true weighted velocity to thereby accurately representvolumetric flow.

Carbon steel for the flanged standpipe 22, and conduit 25 allowscompletion of magnetic field when the sensor 21 is bolted together withthe outer flange 47. Use of non-magnetic stainless steel as in aconventional sensor may not be as effective in producing the desirablyhigh magnetic field. In other words, the carbon steel of the conduit 25results in high density lines of magnetic flux being more efficientlyand evenly distributed over the area of liquid flow. The geometry of themagnetic field is configured such that the measured velocity is morecorrectly weighted to represent true volumetric flow. This advantage isachieved even though the electrodes 35 are situated substantially flushwith the internal diameter of the conduit 25. Consequently, media suchas slurries or those carrying solids or streamers can be reliablymeasured and without substantially impeding flow. In addition, thesensor 21 may operate substantially unaffected by permanent high fatcontent sewage, algae or similar low conductivity coatings of theelectrodes 35.

The flanged standpipe 22 preferably has a dimensional tolerance with thespool piece or conduit 25 such that the sensor 21 and outer flange 28when assembled and bolted to a predetermined torque may beinterchangeable on-site without change of calibration. In other words,the flanged standpipe 22 facilitates original installation andreplacement so that the sensor 21 may inserted into the conduit to thedesired correct depth.

The electromagnetic coil 32 when driven by the desired excitation can bemade to produce little excess heat and, thus, may also be encapsulatedby a potting compound or material 42 to thereby provide resistance tomechanical shock and vibration. The sensor 21 also requires only arelatively low number of coil windings in each coil 32 therebypermitting a substantial reduction in coil size and weight, whilemaintaining and delivering a sufficiently powerful magnetic field withinthe liquid.

For example, as understood with particular reference to FIGS. 5 and 6,an excitation magnetizing current waveform I_(m), as illustrated by plot39a, provides a current of about 0.7 to 1.5 amps peak-to-peak at afrequency in the range of about 5 to 80 Hz that may be delivered byenergy managed electronics of the coil excitation circuit 39. Moreparticularly, the energy managed electronics may include the illustratedcomparator 70, energy storage circuit 71 and transistors 74 connected asshown in FIG. 5. The energy storage circuit 71 creates a high voltagebuild-up to thereby produce a higher magnetizing current I_(m) for agiven coil inductance and frequency as would be readily understood bythose skilled in the art.

The comparator 70 superimposes high frequency pulses on the order of 10KHz to the magnetizing current I_(m) further resulting in a rapidlyoscillating coil voltage V_(coil) as shown by the plot 39b of theenvelope of the coil voltage as would be readily understood by thoseskilled in the art. The coil voltage may have a peak V_(p) of about 70volts, and while the voltage peaks for only a relatively small portionof the waveform on the order of a few milliseconds t_(m) as understoodwith reference to FIG. 6. The excitation of the coil 32 produces asignal V_(gen) at the electrodes 35 as shown by the square wave plot39c. The signal V_(gen) is sampled or measured at predetermined timewindows 39d to produce the output signal as shown by the plot 39e.Accordingly, an advantage of the present invention is that themagnetizing current I_(m) is preferably greater than or equal to about0.7 amps, while the power consumption of the coil 32 is preferably inthe range of about 1 to 6 volt amps. The excitation of the coil 32produces little excess heat so that the power consumption is less than 8VA per sensor including the electronics 39, and as would be readilyunderstood by those skilled in the art. In contrast, a typicalconventional sensor consumes at least 10 VA or more for acceptableaccuracy.

The relatively low power consumption of the sensor 21 of the inventionproduces a negligible temperature rise and consequently allows thelightweight coils 32 to be permanently encapsulated in stiff settingepoxy resin, plastics or other cold or thermosetting potting material 42within the housing 34. The encapsulation or potting material 42 preventson-site vibration or shocks from causing disruptive relative movement ofthe coil 32, electrodes, cabling and other components within housing 34.Hence, the likelihood of vibration and shock errors is significantlyreduced compared to conventional magnetic flow sensors.

An additional sensor 28 may also extend through an opening in the wallof the conduit 25, such as for measuring or sensing one of a number ofother parameters or characteristics related to the liquid within theconduit. For example, the additional sensor 28 may be one of a pHsensor, a salinity sensor, an oxidation reduction potential sensor, adissolved oxygen sensor, and a turbidity sensor. Other or multipleadditional sensors are also contemplated by the present invention.Moreover, because the present invention does not require an electricallyinsulating liner on the wetted surfaces, the additional sensor 35 may bereadily positioned to extend through the wall of the conduit 25. Theadditional sensor 28 may be operatively connected to cooperate with theillustrated processor 30 as would be readily understood by those skilledin the art.

The region or area 19 defined between locations 18a, 18b on the conduitand extending into the interior of the conduit has a relatively weakmagnetic field. For example, the magnetic field adjacent the electrodes35 may typically be greater than about 10 milligauss for the coilexcitation described above. The region 19, in contrast, may have amagnetic field strength of less than about 1 milligauss. The sensor 28may be positioned in a longitudinal extending arcuate portion of theconduit 25 in a range of about 70 to 110 degrees of rotation from animaginary line extending longitudinally through a center of the flowsensor 21 and its associated mounting opening. More preferably, theadditional sensor 28 may be positioned in a longitudinal extendingportion of the conduit 25 at about 90 degrees of rotation from thecenter of the sensor 21. In other words, the electromagnetic coil 32 andthe relative positioning of the opening in the conduit for mounting theadditional sensor 28 with respect to the electromagnetic coil 32produces a relatively weak magnetic field in the region 19 adjacent theadditional sensor 28.

The additional sensor 28 may be a sensor susceptible to magnetic fields,such as a turbidity sensor and a dissolved oxygen sensor, as would bereadily understood by those skilled in the art. Accordingly, placementin the relatively low magnetic field region 19 decreases the likelihoodof undesirable noise being imparted to the sensor 28, while permittingpositioning proximate the liquid flow sensors 21 and along the spoolpiece or conduit 25.

The liquid flow sensors 21 may be positioned in a medial portion of theconduit 25 as illustrated. Accordingly, to provide additionallongitudinal separation and further reduce the magnetic field, theadditional characteristic sensor 28 is preferably positioned adjacent anend of the conduit 25 as shown in the illustrated embodiment. Theconduit 25 may desirably carry all of the sensors needed for theapplication in a compact and easy to install assembly. Multiplecharacteristic sensors 28 may be carried by the conduit 25 as would bereadily understood by those skilled in the art.

The pair of opposing electrodes 35 are positioned on opposite sides onthe liquid contacting portion defined by the covering 37 of the sensorhousing 34. The liquid contacting portion includes an inclined ordownwardly sloping annular portion 34a surrounding a central pressuresensing diaphragm 45. The electrodes 35 of the liquid flow sensor 21 arealso positioned generally flush with an imaginary cylindrical surfacedefined by an interior of the conduit 25. The electrodes 35 contact theflowing media or liquid and generate an electrical signal representativeof the rate of flow of the liquid. In particular, Faraday's Law statesmathematically: Vgenerated =B vd, where Vgenerated is the voltage signalacross the electrodes (typically in millivolts), B is the strength ofmagnetic field (typically in millivolts seconds/ft²), v is the meanvelocity of media (typically in feet per second), and d is the distancebetween electrodes (typically in feet). Accordingly, the relativelylarge spacing between electrodes 35 provides a stronger output signal inaccordance with Faraday's Law.

Yet another advantage of the present invention is that the output signalmay be a linear logarithmic function in terms of pulses per unit volume(ppg) versus flow rate (Q) as given by:

ppg=kQ^(-n), where n and k are determined by calibration.

Accordingly, by linearization of log (ppg)=-n log₁₀ Q+log₁₀ k, arelatively wide and linear range is provided for typical mean velocitiesof 0.1 to 40 feet per second in conduits 25 having a diameter of twoinches or greater. In particular, the bipolar voltage signal from theelectrodes 35 may be converted into a standard 4 to 20 milliamp outputand then converted into pulses for a given volume of liquid flow. Aswould be readily understood by those skilled in the art the pulses arereadily linearized as described above based upon flow rate. Thelinearization and associated calculations may be readily implemented bythe processor 30 as would also be readily understood by those skilled inthe art.

A conductivity or level switch 57 may be mounted at an angle through thesidewall of the conduit 25 dependent on the amount of gas allowable atthe top of conduit when mounted horizontally. In addition, the pair ofsensors 21 may be positioned in vertical relationship so that the levelswitch 57 may be used to switch off an uppermost sensor, as well ascontrol a pump or an alarm as would be readily understood by thoseskilled in the art. The level and mean velocity measurements may bemultiplied and linearized as necessary to provide volumetric flow.

A conventional magnetic flow sensor does not readily lend itself tomeasure parameters, other than flow, from within the sensor unit itselfor from the conduit or spool piece in which the sensor is mounted. Forexample, a non-full pipe flow measurement using a conventional sensormay not be accurate since liquid level measurement cannot readily beaccurately accomplished at the location of the electrodes of theconventional sensor.

Turning now more specifically to FIG. 3, another key feature of theinvention is that the electrodes 35 are preferably fairly largely spacedapart by distance E relative to their depth of penetration C into theconduit. The distance E is also a factor in determining the size of thecoil 32 so that the larger the distance E the larger the diameter of thecoil 32 may be made, thereby producing a wider magnetic field. The ratioof E/C is desirably above a predetermined value, such as 2 to 1, andmore preferably above 3 to 1, to enhance accuracy. The electrode spacingE is preferably greater than 10% of the diameter of the conduit 25. Moreparticularly, it has been found that for a conduit 25 diameter of lessthan about 36 inches, the electrode separation distance E is preferablynot less than about 20% of the diameter D. For a conduit diameter Dgreater than about 36 inches, but still less than 80 inches, E ispreferably not less than 10% of the diameter.

Increased accuracy is provided by the relatively large ratio of thedistance between the electrodes E compared to the chordal depth C of thesensor 21, along with the enhanced magnetic field, in turn, derived froma relatively high magnetizing current and frequency along with themagnetically permeable material of the conduit 25.

Another aspect of the invention is that the depth of sensor penetrationinto the interior of the pipe helps to change the flow profile of themedia to be more regular. The minimum ratio of E/C adequately conditionsirregular velocity flow profiles to provide greater accuracy. Inaddition, the depth of penetration C is also preferably not more thanabout 10% of the diameter D. These relationships are advantageous inassuring high accuracy with a relatively compact sensor 21.

The minimum ratio of E/C of greater than 2/1 still allows virtuallyunrestricted free flow of liquid in the spool piece or conduit 25 andwith negligible pressure loss. The ratio also improves irregularitiesoccurring in velocity profiles due to potentially unfavorable upstreamand downstream mating pipe configurations.

It is recognized that one of the largest sources of error experienced byconventional flow sensors is related to relatively weak magnetic fieldstrength and its distribution within the area of flow. That coupled withunfavorable upstream and downstream mating pipe conditions, such as pipebends, means that conventional sensors often compromise the accuracy ofthe true weighted signal across the electrodes to infer volumetric flow.The apparatus 20 and sensors 21 according to the invention overcomethese shortcomings of conventional sensors.

Returning again now more particularly to FIG. 4, the sensor 21 includesa pressure plate 44 to ensure that the sensor is correctly supported towithstand static pressures within the spool piece 22. The illustratedsensor 21 also includes a central pressure sensing diaphragm 45connected in fluid communication with a pressure sensing transducer 55.Accordingly, the invention may be used to determine if the pipe orconduit 25 is less than full, or to determine the pressure within a fullpipe.

The relatively large separation distance of the electrodes 35 and therelatively large diameter of the coil 32 permits a relatively largepressure or level sensing diaphragm 45 and associated components to befitted at the center of the sensor 21. The pressure sensing diaphragm 45may preferably be manufactured from media compatible material, and morepreferably, electrically conductive material to permit the diaphragm toserve as a ground electrode. The diaphragm 45 may be coupled to apressure sensing assembly 48 positioned within an internal cavity 49which, in turn, may be oil filled to communicate with a remote orintegral pressure/level transducer or gauge 55 as would be readilyunderstood by those skilled in the art. The pressure sensing assembly 48may also be replaced by an integrally fitted pressure/level transduceror by an electrode for electrical grounding, as would also be readilyunderstood by those skilled in the art.

In other words, the apparatus 20 may include pressure sensing meansprovided by a transducer operatively connected to the pressureresponsive diaphragm 45 for generating a signal relating to liquidpressure. The pressure sensing means may also include indicator meansfor providing an indication of at least one of liquid pressure if theconduit is full, and liquid level if the conduit is less than full orhas an open upper portion. For example, a standard pressure gauge 55 maybe connected in fluid communication with the cavity adjacent thepressure responsive diaphragm. Alternately, a transducer may deliver itsoutput signal to the processor 30 to facilitate computation of thevolumetric liquid flow. Accordingly, a compact and reliable sensor forboth liquid flow rate and liquid pressure is provided by the presentinvention.

A filler material 33 or part of the mold of a liner may be positionedadjacent the outer edges of the electrodes 35. As would be readilyunderstood by those skilled in the art, the conduit 25 may include aliner 49 suitable for use with potable water or for compatibility withcorrosive media, for example. However, the liner 49 may be damagedwithout affecting measurement accuracy for the sensor 21. In contrast,in a conventional sensor any damage to the liner is likely todetrimentally affect performance. In other words, even when a liner 49is used in the apparatus 20 of the present invention, it is not criticalthat the media be kept from penetrating between the conduit 25 and theliner 49.

The illustrated sensor 21 includes a molded covering 37 which surroundsthe electrodes 35 and extends into the recess adjacent the electrode 35for efficient high pressure sealing. In other embodiments of the sensor,the covering 20 may not be needed, such as where plastic or otherelectrical insulation material, such as PVC, is used to define theliquid contacting portion of the sensor. A body 46 of material, such asplastic, non-magnetic stainless steel or aluminum, may underlie theillustrated insulating covering 37.

Two separate seals 50, 51 trap a shim 52 therebetween for the electrode35. The shim 52 is preferably welded to the electrode 35. The electrodes35 and the seals 50, 51 are preferably made from media compatiblematerial as would be readily understood by those skilled in the art. Theelectrodes 35 may also be used for measurement of velocity, electricalconductivity, or media salinity, for example, in addition to sensingflow rate, as would also be readily understood by those skilled in theart.

A core 40 of carbon steel or sintered soft iron particles is preferablycontained in electrically insulated bags as would be readily understoodby those skilled in the art. The core 40 links the magnetic field withthe adjacent conduit portions. The core 40 also preferably defines a gapof about 1/8 inch with the coil 32. Such a construction of core 40improves the efficiency of penetrating the media with magnetic flux, andreduces detrimental effects of eddy currents.

Grounding screws 38 are provided to ensure that all internal electricalgrounding components have the same electrical potential to the outerflange 23 and the conduit 25. In addition, an electrical grounding plate39 is also provided for grounding the pressure/level diaphragm assemblyto all other internal electrical grounding. Various seals 51, such as ofrubber or Kalrez may be used in the sensor 21 as shown in theillustrated embodiment.

Turning now additionally to FIGS. 7 and 8, another embodiment of thesensor 21' is described. In this embodiment, the liner has been omittedas the liner is optional according to an advantage of the presentinvention. The plastic body 46 and pressure plate 44 have also beenomitted. The function of the pressure plate is provided by theillustrated flange 47'. The mold material 42' that encapsulates theelectrodes 35', pressure/level sensing assembly 48', coil 32', core 40'and other components may be cold setting or thermosetting syntheticmaterial, such as epoxy resin, Polyurethane, PFA, or similar materialsas will be readily appreciated by those skilled in the art.

The outer flange 47 being an integral part of sensor 21' may be boltedto the standpipe flange 23' with a predetermined torque. This feature ofthe invention, together with normal control of manufacturing tolerancesand other features as described above allows interchangeability of thesensor with the conduit 25 on-site without typically requiring a changein sensor calibration. This configuration also allows the thickness ofsensor 21' to be relatively slim, that is, typically less than 11/2. Theslim shape is important particularly when the sensor 21' is used in openchannels as discussed in greater detail below.

Each electrode 35' may be provided by an electrode tip 35a which isscrewed into an electrode extension 35b normally after molding of themold or potting material 42'. The tip or outermost portion of theelectrodes 35' are desirably positioned to extend outwardly beyond theadjacent downwardly sloping annular housing portion 34a' as shownperhaps best in FIG. 7. Moreover, the outermost electrode portions arepreferably substantially flush with an imaginary plane defined by thecentral portion of the housing provided by the illustrated pressuresensing diaphragm 45'.

An O-ring seal 64 may be provided as shown in the illustratedembodiment. Rotation of electrode extension 35b is prevented by a pin 65protruding from the electrode extension into the hard set mold orpotting material 42'. A connecting wire may be attached to the electrodeconnection pin 66. A cylindrical electrode screen 67 shields theelectrode extensions 35b from electrical interference that may begenerated by the electromagnetic coil 32'.

As shown in FIGS. 8-10, a further reason that measurement accuracy isenhanced at relatively low velocities typically less than two feet persecond is that small transversely extending ridges or serrations 62 maybe provided in the curved or sloping profile at each end of the sensor21'. The serrations 62 provide velocity profile enhancing means forincreasing the effective Reynolds Number at the liquid contactingportion of the sensor housing 34'. The serrations 62 may define asawtooth cross-sectional shape and may be about 1/16"×1/16"×45°. Theserrations 62 may have a vertical height in the range of about 1/16 to3/8 inches. The serrations 62 may be formed by molding or a subsequentcutting or forming operation as would be readily understood by thoseskilled in the art. The serrations 62 may also be molded or formed intothe filler 33' adjacent the edges of the opening in the conduit, as wellas the area in the area around the electrodes 35'.

As shown in FIG. 8, the serrations 62 extend parallel to a directiondefined by the electrodes 35'. The serrations 62 are also illustrativelyarranged in two bands 62a, 62b extending adjacent opposite side edges ofthe liquid contacting portion of the sensor housing 34'. Each band 62a,62b includes a gap in the ridges or serrations adjacent the respectiveelectrodes 35'. As shown in FIGS. 9 and 10, the serrations 62' mayextend across the entire liquid contacting portion 34" of a sensor,particularly for relatively small diameter conduits 25'. Otherconfigurations of projections to increase the Reynolds number adjacentthe electrodes 35' are also contemplated by the invention as would bereadily understood by those skilled in the art.

The serrations 62 cooperate with the geometric relationships describedabove including the curved profile and particularly the ratio of E/C orE/W to condition an irregular velocity profile 68a into a more regularprofile 68b in the area adjacent the pair of illustrated sensors 21' asshown perhaps best in the schematic views of FIGS. 9 and 10. Thesefeatures together with the strong magnetic field in the liquid producedby the sensor according to the invention provides highly accuratevolumetric flow measurements. It is a fundamental advantage that theinvention can operate with acceptable accuracy within or near laminarflow regimes, typically at Reynolds Numbers 600-6000, as well asReynolds Numbers substantially into the turbulent flow regime, typicallyup to 20 million.

In the embodiment of the apparatus 20 (FIG. 1) including the pair ofsensors 21 mounted diametrically opposite each other in a circularcross-sectional carbon steel spool piece or conduit 25, each of thesensors includes a relatively large diameter coil 32 and pair ofelectrodes 35 of relative large distance apart compared to conventionalinsertion type sensors. Such a quadruple electrode arrangement withcoils virtually parallel to one another and with the liquid contactingportion of the sensors 21 projecting into the conduit a predetermineddistance serves to condition an irregular velocity profile andefficiently distribute the magnetic field. This provides accuratedetermination of the volumetric flow down to mean velocities the same orlower than conventional magnetic flow sensors, but with lower costs ofconstruction and substantially lower velocities and better accuraciesthan conventional magnetic flow sensors.

Referring now additionally to FIG. 11 an open channel embodiment of theapparatus 21" of the invention is described. In this embodiment, acarbon steel cradle or portion of the open channel 60 defines the liquidpassageway 61. The illustrated passageway 61 and cradle or channel 60have a rectangular cross-sectional shape. Those of skill in the art willrecognize that other cross-sectional shapes are also contemplated by theinvention and that such channels are often formed or installed in theground as illustrated.

The sensor 21' is connected to the cradle or channel 60 to provide asufficiently strong magnetic field within the media or liquid. For anopen channel configuration with a width W of less than about 80 inches,the separation between electrodes E is preferably between about 95% and10% of the width. This embodiment of the apparatus 65 may also includethe pressure sensing diaphragm and other components as described abovewith respect to the other invention embodiments as will be readilyappreciated by those skilled in the art. In addition, multiple sensors21" may also be used in an open channel configuration.

Single or multiple sensors 21" may be used in the open channelconfiguration without the need for a cross-sectional restriction in theflow channel width where the ratio of E/W is as provided above. Thedistance between electrodes 35" to the width of the open channel is thussufficiently large that the sensor accurately 21" infers volumetric flowwith high accuracy.

In summary, because of the relatively lightweight and compact nature ofthe sensor 21, 21' according to the invention, a relatively short spoolpiece or conduit 25 may be used to mate with adjacent conduit sections.In addition, because the sensor 21, 21' may be mounted in a carbon steelspool piece or conduit 25 that does not require lining, the followingadvantages are possible: end flanges are not necessary and the conduitcan be readily joined to adjacent sections; and additional pH,electrical conductivity, salinity, oxygen reduction potential, density,dissolved oxygen, turbidity and similar sensors may be mounted in thesame carbon steel spool piece.

The liquid flow sensor 21, 21' according to the invention also providesa demountable, virtually obstructionless magnetic flowmeter which may bereadily installed into an existing pipe, venturi, in a pipe fittedcarbon steel spool piece, or in a cradle in an open channel or non-fullpipe. The sensor 21, 21' uses a relatively large magnetizing current,and low power consumption to provide cost effective improvements overconventional magnetic flow sensors. The mechanical design of the sensor21, 21' incorporates lightweight coils 32, encapsulated in a stiffsetting plastic or resin potting material 42, and while the coils 32provide a relatively high magnetic field. The sensor 21, 21'incorporates a large ratio of coil diameter and distance across theelectrodes 35 compared to the inserted distance when installed.Accordingly, relatively high accuracy is provided by the presentinvention.

The sensor 21, 21' includes a coil 32 and electrodes 35 in a singlemodule that may be field replaceable and interchangeable with spares andmanufactured to tolerances that allow interchangeability with spares,without the need to recalibrate. The sensor 21, 21' may also include anintegral grounding electrode or pressure or level sensing diaphragm 45,which acts simultaneously as a grounding electrode, such that externalor further means of grounding may not be necessary. The accuracy of thesensor 21, 21' is largely unaffected by cuts or scratches in anyinsulating liner or coating for the interior of the liquid carryingconduit. The liquid flow sensor 21, 21' may also be included in arelatively low cost said carbon steel conduit.

Many modifications and other embodiments of the invention will come tothe mind of one skilled in the art having the benefit of the teachingspresented in the foregoing descriptions and the associated drawings.Therefore, it is to be understood that the invention is not to belimited to the specific embodiments disclosed, and that modificationsand embodiments are intended to be included within the scope of theappended claims.

That which is claimed is:
 1. An apparatus for measuring liquid flowrate, said apparatus comprising:an open channel for carrying a liquidflow, said open channel having an open upper portion, a cross-section ofa predetermined width, a bottom wall, and an opening in the bottom wall;means for measuring the fluid height in the open channel; and a liquidflow sensor positioned in the opening in said open channel, said liquidflow sensor comprisinga housing comprising a liquid contacting portionextending generally parallel to an axis of said open channel and beingpositioned to extend into an interior of said open channel, wherein saidliquid contacting portion comprises a generally planar central portionand a downwardly sloping annular portion surrounding the centralportion, an electromagnetic coil positioned in said housing forgenerating a magnetic field within the liquid flow, and a pair of spacedapart electrodes carried by said downwardly sloping annular portionadjacent respective opposite edges thereof, wherein said electrodesextend outwardly from the downwardly sloping annular portion and areexposed on the liquid contacting portion for generating a signal relatedto liquid flow rate, said electrodes defining a distance therebetweenbeing in a range of about 0.10 to 0.95 times the predetermined width ofthe open channel.
 2. An apparatus according to claim 1 wherein said pairof electrodes are positioned adjacent respective opposite edges of theliquid contacting portion of said housing.
 3. An apparatus according toclaim 1 wherein outermost portions of said electrodes are substantiallyflush with an imaginary plane defined by the central portion.
 4. Anapparatus according to claim 1 wherein said open channel comprises amagnetically permeable material so that said electromagnetic coil ofsaid liquid flow sensor cooperates with the magnetically permeablematerial of said open channel to generate the magnetic field within theliquid flow.
 5. An apparatus according to claim 4 wherein said openchannel has a generally rectangular transverse cross-section.
 6. Anapparatus according to claim 5 wherein said liquid flow sensor furthercomprises flux path means for defining a magnetic flux path from saidcoil and through adjacent portions of said open channel.
 7. An apparatusaccording to claim 1 further comprising excitation means for poweringsaid electromagnetic coil with a waveform having a peak-to-peak currentof greater than or equable to about 0.7 amps, and at a power in a rangeof about 1 to 6 volt amps.
 8. An apparatus according to claim 1 whereinsaid liquid contacting portion further comprises a grounding electrodefor contacting the liquid flow.
 9. An apparatus according to claim 1wherein said liquid flow sensor further comprises potting means forsecuring said electromagnetic coil within said housing.
 10. An apparatusfor sensing liquid flow rate and comprising:a housing comprising aliquid contacting portion for extending generally parallel to a liquidflow in a channel and being positioned to extend into the liquid flow,said liquid contacting portion comprising a central generally planarportion and a downwardly sloping annular portion surrounding the centralportion; means for measuring the flow height in a channel; anelectromagnetic coil positioned in said housing for generating amagnetic field within a liquid flow; potting means for securing saidelectromagnetic coil within said housing; excitation means for poweringsaid electromagnetic coil with a waveform having a peak-to-peak currentof greater than or equal to about 0.7 amps, and at power in a range ofabout 1-6 volt amps; and a pair of spaced apart electrodes carried bysaid downwardly sloping annular portion adjacent respective oppositeedges thereof for generating a signal relating to the liquid flow rate.11. An apparatus according to claim 10 wherein outermost portions ofsaid pair of electrodes are substantially flush with an imaginary planedefined by the central portion.
 12. An apparatus according to claim 10further comprising a magnetically permeable core positioned within saidelectromagnetic coil.
 13. An apparatus according to claim 10 whereinsaid liquid contacting portion comprises a grounding electrode forcontacting the liquid flow.
 14. An apparatus according to claim 10wherein said electrodes are positioned outside of an imaginary cylinderdefined by outermost portions of said electromagnetic coil.
 15. Anapparatus for sensing liquid flow rate and comprising:a housingcomprising a liquid contacting portion for extending generally parallelto a liquid flow in a channel and being positioned to extend into theliquid flow; means for measuring the flow height in a channel; anelectromagnetic coil positioned in said housing for generating amagnetic field within the liquid flow; potting means for securing saidelectromagnetic coil within said housing; excitation means for poweringsaid electromagnetic coil with a waveform having a peak-to-peak currentof greater than or equal to about 0.7 amps, and at a power in a range ofabout 1 to 6 volt amps; and a pair of spaced apart electrodes carried bythe liquid contacting portion adjacent respective opposite edges thereoffor generating a signal relating to the liquid flow rate.
 16. Anapparatus according to claim 15 wherein said liquid contacting portioncomprises a central generally planar portion and a downwardly slopingannular portion surrounding the central portion; and wherein saidelectrodes are positioned on said downwardly sloping annular portion.17. An apparatus according to claim 16 wherein outermost portions ofsaid pair of electrodes are substantially flush with an imaginary planedefined by the central portion.
 18. An apparatus according to claim 15further comprising a magnetically permeable core positioned within saidelectromagnetic coil.
 19. An apparatus according to claim 15 whereinsaid liquid contacting portion further comprises a grounding electrodefor contacting the liquid flow.
 20. An apparatus according to claim 15wherein said electrodes are positioned outside of an imaginary cylinderdefined by outermost portions of said electromagnetic coil.
 21. A methodfor sensing liquid flow rate comprising the steps of:providing an openchannel for carrying a liquid flow, said open channel having across-section of a predetermined width and an opening in a bottom wallthereof; measuring the fluid height in the open channel; positioning aliquid flow sensor in the opening in said open channel so that a liquidcontacting portion extends generally parallel to an axis of said openchannel and extends into an interior of said open channel, said liquidflow sensor further comprising an electromagnetic coil for generating amagnetic field within the liquid flow, and a pair of spaced apartelectrodes being exposed on the liquid contacting portion for generatinga signal related to liquid flow rate, and wherein said electrodes definea distance therebetween being in a range of about 0.10 to 0.95 times thepredetermined width of the open channel, and powering theelectromagnetic coil with a waveform having a peak-to-peak current ofgreater than or equal to about 0-7 amps, and in a range of about 1-6volt amps, and then calculating the flow rate.
 22. A method according toclaim 21 wherein the step of providing said open channel comprisesproviding a magnetically permeable open channel so that saidelectromagnetic coil cooperates with the magnetically permeable openchannel to generate the magnetic field within the liquid flow.
 23. Amethod according to claim 21 further comprising the step of generatingan output based upon a linear logarithmic relationship betweenintegrated pulse output per unit volume flow versus flow rate.
 24. Amethod according to claim 21 wherein the step of providing the openchannel comprises providing an open channel having a generallyrectangular transverse cross-section.